What is 1/2 log_{2}(5)-2log_{2}(7) ?

The solution to 1/2 log_{2}(5)-2log_{2}(7) is log_{2}((sqrt(5))/(49))

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simplify 1/2 log_{2}(5)-2log_{2}(7)

simplify

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (7)

lo g_{2} (\frac{5}{49})

Decimal Notation

- 4.45374 \dots

Solution steps

\frac{1}{2} lo g_{2} (5) - 2 lo g_{2} (7)

\frac{1}{2} lo g_{2} (5) = lo g_{2} (5^{\frac{1}{2}})

- 2 lo g_{2} (7) = - lo g_{2} (7^{2})

= lo g_{2} (5^{\frac{1}{2}}) - lo g_{2} (7^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (5^{\frac{1}{2}}) - lo g_{2} (7^{2}) = lo g_{2} (\frac{5 ^{\frac{1}{2}}}{7 ^{2}})

= lo g_{2} (\frac{5 ^{\frac{1}{2}}}{7 ^{2}})

7^{2} = 49

= lo g_{2} (\frac{5 ^{\frac{1}{2}}}{49})

Apply exponent rule:

a^{\frac{1}{2}} = a

5^{\frac{1}{2}} = 5

= lo g_{2} (\frac{5}{49})

lo g_{3} (81 x)

ln (\frac{5}{6})

lo g_{10} (\frac{x ^{2}}{y ^{5}})

2 ln (x) + 4 ln (y) - 3 ln (z)

ln (x) + ln (3)

What is 1/2 log_{2}(5)-2log_{2}(7) ?
The solution to 1/2 log_{2}(5)-2log_{2}(7) is log_{2}((sqrt(5))/(49))